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www.us-tech.com Heavy Copper Design Considerations: Part 1 Continued from previous page
about 5 ppm/°C. However, the epoxy resin of
a low Tg glass-epoxy laminate will expand at a rate of 350 ppm/°C above the Tg. It doesn’t take much imagination to under- stand that the epoxy glass sub- strate is much like “rats leaving
If the plated copper is too thin (typically less than 1 mil or 25.4µ) then the z-axis stress can fracture the copper barrel.
Internal vs. External Why are there curves for
internal traces and external traces? The reference chart
equation of Ohm’s law and the volume resistivity of copper to cal- culate maximum current at a given temperature, I = K
l l dT0.44 (W H)0.725, where I equals maxi-
mum current, dT equals tempera- ture rise, W equals trace width in mils, H equals trace thickness in mils, and K is either 0.024 for the inner layer or 0.048 for the outer layer.
The factor that seems to be
er a required current at a known temperature rise above ambient (for example, 20°C rise). The assumption of the designer would be that the resulting traces are “rectangular.” They are not!
Trapezoidal Traces In the following micro-sec-
tion picture (Figure 2), a 13 oz inner layer trace was measured after the etch process. Note that
October, 2021
Figure 1: a chart from IPC 2221 showing required cross sectional area to maintain constant temperature.
a sinking ship” when the copper begins to heat (the epoxy expands much more than the copper). If the expected tempera- ture rise in the copper traces exceeds the decomposition time/temperature of the glass epoxy laminate, then at some point, the PCB will fail. Mass loss is only one of the
failure possibilities with thermal expansion. De-lamination typical- ly happens before the mass loss reaches 5 percent. During ther- mal expansion of the laminate, there is enormous z-axis stress on the copper barrels of the via holes.
shows the curves for an external trace. However, the chart for internal traces is much different as the traces must be almost two times the cross-sectional area to maintain the same temperature rise above ambient when the cur- rent is equal. The logic is that you must reduce the heat in the trace by reducing the resistance of the trace. Keep in mind, the power in a
resistive element is directly pro- portional to resistance, and power loss is what creates internal heat- ing. IPC-2221 contains a formula that was derived from the power
Figure 2: micro-section of a 13 oz inner layer, showing a trapezoidal shape with curved sides.
overlooked is that this chart and the equation are based on “cross- sectional area” of the copper trace. Within a reasonable range of currents and cross-sectional area, this equation is fairly accu- rate. What the chart and the equation (very cleverly) avoid is providing the designer with a trace width vs. copper weight. Therefore, a designer that
does not have an intimate knowl- edge of the PCB fabrication process could easily convert this equation into a chart of copper weight (in ounces) vs. trace width (in mils). The designer would believe that this chart would deliv-
the 13 oz inner layer results in a copper thickness of approximate- ly 18 mils (0.018071 in.). This is the result of converting ounces into mils of thickness. The correct conversion is 1
oz = 1.37 mils. Therefore, 13 ounces should convert to a thick- ness of 17.81 mils (0.01781 in.). It should also be noted that the tolerance of the thickness grows with the increasing ounces. The fabricator adjusted
their process (called “etch com- pensation) to make the “foot” (the base of the trace) equal the trace thickness in the designer’s Gerber file. However, the result- ing trace is not a rectangle, but a trapezoid with curved sides, making this figure much more difficult to precisely calculate the cross-sectional area. To do so with precision
requires the use of a Fourier analysis of the trapezoid to con- sider the two curved sides. I am not sure I can still do that with- out embarrassing myself, so I opted to convert the curved sides into identical right triangles and used conventional geometric cal- culations for the cross-sectional area of the trace. Part two of this guide will
discuss how to deal with the vari- ables that have been discussed, including a suggested design process for heavy copper and information allowing a designer to more precisely select the trace width to yield the desired cross- sectional area. Contact: ICAPE USA, 8102
Zionsville Road, Indianapolis, IN 46268 % 317-405-9427 Web:
www.icapeusa.com
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